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Table 2.

Nucleus State Transition Tt/t B(E2) ( ? 0 10- 2 4 cm 2 ß 1 / r i g . /irr. Enhance-Energy Present Work e- 10~48 cm4 keV s2 keV s2 keV s2 ment (keV) IO"3 9 IO"39 IO"39 Factor

2 + 121.78 (1.35±.05) ns 0.737±.027 6.084 .318 11.14 28.97 2.4 215 4 + 244 (42± 18) ps 1.373±.6 8.304 .360 5.54 29.29 3.04 271

symmetric rotator. The contribution of the rigid and the irrotational part of the mot ion depends on the nuclear deformation parameter ß. W h e n the de-

1 M . GOLDHABER and A . W . SUNYAR, P h y s . R e v . 8 3 , 9 0 6 [1951].

2 J. RAINWATER, Phys. Rev. 79, 432 [1950]. 3 A . BOHR and B. R . MOTTELSON, Dan . M a t . Fys . M e d d . 2 7 ,

No. 16 [1953]. 4 A . S. DAVYDOV and A . A . CHABAN, N u c l . P h y s . 2 0 , 4 9 9

[ I 9 6 0 ] . 5 T . R . GERHOLM and J. LINDSKOG, A r k . Fys . 2 4 , 1 7 1 [ 1 9 6 3 ] . 6 Z . AWWAD, O. E. BADAWY, M . R . EL-AASSER. and A . H .

EL-FARRASH, in Course of Publication. 7 J. LINDSKOG and T . SUNDSTROM, A r k . Fys . 2 4 , 1 9 9 [ 1 9 6 3 ] . 8 A. W. SUNYAR. Phys. Rev. 98, 653 [1955].

formation is small, only the irrotational motion will dominate and when the deformation is large only the rigid mot ion will dominate.

9 D . B . FOSSAN and B . HERSKIND, N u c l . Phys . 4 0 , 2 4 [ 1 9 6 3 ] . 10 M . BIRK, G . GOLDRING, and Y . WALFSON, Phys . R e v . 1 1 6 ,

730 [1959]. 11 A. HÜBNER, Z. Physik 183,25 [1965]. 12 R . M . DIAMOND, F . S. STEPHENS, R . NORDHAGEN, and K .

NAKAI, Phys. Rev. C 3, (No. 1), 344 [1971]. 13 D. G. ALKHAZOV, Bull. Acad. Sei. USSR 28, 146 [1964], 14 R.S.HAGER and E.C.SELTZER, Internal Conversion Tables,

Calt 63-60 AEC Research and Development Report. 13 R . B . MOORE and C. WHITE, J. P h y s i c s 3 8 , 1 1 4 9 [ 1 9 6 0 ] . 16 K . ALDER, A . BOHR, T . HUUS, B . MOTTELSON, and A . W I N -

THER, Rev. Mod. Phys. 28, 432 [1956].

Relaxation of Diffused Zinc Atoms During Short-Range-Ordering in Cu-30% Zn Alloy

T . H . Y O U S S E F

National Research Centre, Dokki, Cairo

(Z. Naturforsch. 27 a, 1232—1234 [1972] ; received 4 April 1972)

The internal friction which is a diffusion dependent physical property has been used as a means to determine the kinetics of short range order in (Cu-30% Zn) alloy. Curves of relative (Q~l/Q0~1) against annealing time have been plotted for various annealing temperatures. An average activation energy of 1.7 eV was found for the ordering process, which is equal to the activation energy for zinc diffusion in coarse grained copper.

When an alloy having short range order ( S R O ) , is quenched f r o m high temperatures, excess vacan-cies are liberated which will enhance di f fusion, and hence the ordering rate during subsequent anneal-ing. Due to this enhanced ordering rate, the equi-l ibrium degree of short range order canbe achieved in reasonable times even at rather low temperatures, provided that vacancies are mobi le at these tempera-tures. F o r copper-zinc alloys in the alpha phase, the existence of S R O has been theoretically 1 establish-ed and experimentally demonstrated by many wor-kers (c f . CLAREBROUGH et a l . 2 ) . Evidence f r o m diffuse X-ray and /or neutron scattering experiments is not available because of the small dif ference in scattering power of copper and zinc 3 atoms. L o n g

range order in alpha brass above — 30 ° C is im-probable 3 because of the rather low ordering en-ergy of the system.

1. Experimental Procedure and Results

Internal friction experiments were carried out using a torsion pendulum (test wire dia. 1 mm, length 6 cm) . The free decay of the oscillations was observed at fre-quency 0.7 c/sec and strain amplitude 1 x 10~4 . The torsion pendulum is kept at 2 x 1 0 - 5 mm Hg vacuum.

Specimens used were prepared from high purity cop-per and zinc. The appropriate proportions of the two comonents were melted in closed graphite molds me-chanically agitated for homogenization. The solid solu-tions were cold drawn into wires of 1 mm diameter. Subsequent chemical analysis allowed the precise de-

termination of the zinc content. The specimens were given pre-anneal at 600 °C for 1 hour to produce rela-tively coarse grains ( ^ 0.2 mm) in order to eliminate relaxation by grain boundary diffusion.

The existence of SRO in the specimens was tested by measuring the change of internal friction at tem-peratures up to 500 °C. Results are shown in Figure 1. The peak in Fig. 1 shifts towards lower temperature as the zinc content in the specimen increases. Measure-

2 -

5 Cfc ki

Cu -30*/» Zn

-20% Zn

-15V, Zn

0 200 400 600 TEMPERATURE (°C)

Fig. 1. The variation of the internal friction of annealed alloy specimens with temperature. The peaks demonstrate the exis-

tence of short-range order.

ments of the temperature dependence of internal fric-tion were made in ordered and disordered specimens of Cu-30% Zn alloy. Ordering was effected by anneal-ing at 560 °C for 1 hour, followed by slow cooling last-ing for 6 hours, disordering by heating at 560 °C for 10 minutes, and immediate quenching in cold water (20 ° C ) . Care was taken that no appreciable heat treat-ment was given to disordered specimens during the course of measurements. This was ensured by working at relatively low temperatures, and by keeping the specimen at the furnace temperature for the shortest possible time. Moreover, after each reading the speci-men was requenched in order to bring the disordering condition to the same initial state. The results, shown in Fig. 2, indicate that the internal friction in the or-dered state is higher than in the disordered state.

The disorder-order transition in Cu-30% Zn was f o l l owed b y plotting the relative isothermal internal fr ict ion ( Q ~ 1 / Q o ~ 1 ) f o r initially disordered samples against the effective reaction time, t, f o r constant an-nealing temperatures between 2 0 0 , 2 6 0 ° C the internal fr ict ion of a disordered sample at zero

E ' annealed

quenched

0 100 200 300 TEMPERATURE (°C)

Fig. 2. Temperature dependence of the internal friction of annealed and quenched Cu-30% Zn alloy.

2 3 10 10 10

EFFECTIVE ANNEALING TIME ( t ) min.

Fig. 3. Relative isothermal internal friction/time curves for ordering in Cu-30% Zn.

10*

10

I I I I

Q-'/Q-Jtl.d 1,6 4

-

/ / / S ] ' 2

* 1 1 1,9 2.0

1000/T ( T,°K) 2,1

Fig. 4. Equivalent times and temperatures for the ordering process in Cu-303> Zn.

annealing time, and Q t h a t after isothermal an-nealing for the corresponding time and temperature). Typical results are shown in Figure 3. It must be noted that after finishing isothermal annealing at every temperature the specimen was requenched to bring it to an identical state as judged by constant values of internal friction at the beginning of each annealing run.

Equivalent times and temperatures for the order-ing process as derived f rom Fig. 3 are illustrated in Figure 4. Each curve corresponds to a given value of (Q-1/Qo~1)* Thev are parallel straight lines in-dependent of the value of a n d give an activation energy of 1.7 eV for the SRO process.

2. Discussion

In accord to current theories which attribute an elastic effect in substitutional solid solutions to stress-induced changes in local order, the results in Fig. 1 support the view that SRO occurs in the tested speci-mens. Since the ordering process is a manifestation

1 L. GUTMAN, Trans . A I M E 1 7 5 , 1 7 8 [ 1 9 4 8 ] . 2 L . M . CLAREBROUGH, M . E. HARGRAVES, and M . H . L o -

RETTO, P r o c . R o y . S o c . L o n d o n A 2 5 7 , 3 2 6 [ 1 9 5 0 ] ; A 2 6 1 , 500 [1961].

3 D. T . KEATING, A c t a M e t . 2 , 885 [ 1 9 5 4 ] .

of solute atom diffusion, it is achieved more easily as the zinc content is increased. The relaxation pro-cess thus operates at lower temperature as found in Fig. 1, and this agrees with the increase in diffusion rate with increasing zinc content in copper-zinc al-loys as has been reported by HINO et al. 4 . The peak height shown in Fig. 1 might be taken as a measure of the relaxation strength. It increases with increas-ing zinc content. This may be explained on the basis that vacancies are created by heating which increase the zinc diffusion rates and thus enhances SRO. The observed suppression of this relaxation in the cases of low zinc content could be due to the decreasing number of centers of SRO. This conclusion is sup-ported by TAMMANN'S 5 observations on resistivity changes in copper-zinc alloys.

The value of 1.7 eV for the activation energy for SRO in Cu-30/o Zn is in reasonable agreement with the values given in the literature obtained f rom mea-surement of other physical properties (e. g. see LANG et al. 6 ) . It also agrees well with the activation en-ergy for zinc diffusion in coarse grained Cu

4 J .HINO, C.TOMIZUKA, and C.WERT, A c t a M e t . 5 , 41 [ 1 9 5 7 ] . 5 G. TAMMANN, Z. Metallkunde 28, 6 [1936]. 6 E. LANG and W . SCHULE, Z . M e t a l l k u n d e 6 1 , 866 [ 1 9 7 0 ] . 7 R . FLANAGAN and R . SMOHRCHAWSKI, J. A p p l . Phys . 2 3 ,

785 [1952].